Answer:
![y=3x+2](https://tex.z-dn.net/?f=y%3D3x%2B2)
Step-by-step explanation:
To find the equation, use the slope-intercept formula:
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
m is the slope and b is the y-intercept. Now, it'll really help to draw a line through the points, connecting them. If you look at point (0,2), we can see that this is the y-intercept (where a point sits on the y-axis when x=0). You can insert this into the equation by taking the y value:
![(0,2)\\y=mx+2](https://tex.z-dn.net/?f=%280%2C2%29%5C%5Cy%3Dmx%2B2)
Now, take any two points to find the slope. To make it easier, I'll use (1,5) and (0,2). Use the slope formula for when you know two points:
![\frac{y(2)-y(1)}{x(2)-(x1)} =\frac{rise}{run}](https://tex.z-dn.net/?f=%5Cfrac%7By%282%29-y%281%29%7D%7Bx%282%29-%28x1%29%7D%20%3D%5Cfrac%7Brise%7D%7Brun%7D)
Rise over run is the change in the y-axis over the change in the x-axis. Insert values:
![(1(x1),5(y1))\\(0(x2),2(y2))\\\\\frac{2-5}{0-1}](https://tex.z-dn.net/?f=%281%28x1%29%2C5%28y1%29%29%5C%5C%280%28x2%29%2C2%28y2%29%29%5C%5C%5C%5C%5Cfrac%7B2-5%7D%7B0-1%7D)
Solve:
![\frac{2-5}{0-1}=\frac{-3}{-1}](https://tex.z-dn.net/?f=%5Cfrac%7B2-5%7D%7B0-1%7D%3D%5Cfrac%7B-3%7D%7B-1%7D)
Since both are negative, the result is a positive:
![\frac{-3}{-1}=\frac{3}{1} =3](https://tex.z-dn.net/?f=%5Cfrac%7B-3%7D%7B-1%7D%3D%5Cfrac%7B3%7D%7B1%7D%20%3D3)
Insert this into the equation as m, the slope:
![y=3x+2](https://tex.z-dn.net/?f=y%3D3x%2B2)
Done.
48/14 = 24/7
24/7 times 14 equals 48
Answer:
125a^3 + 300a^2b + 240ab^2 + 64b^3
Step-by-step explanation:
The volume of a cube is the cube of the side length.
V = s^3
Here, the side length of the cube is 5a + 4b, so we cube 5a + 4b.
V = (5a + 4b)^3
V = (5a + 4b)(5a + 4b)(5a + 4b)
V = (25a^2 + 20ab + 20ab + 16b^2)(5a + 4b)
V = (25a^2 + 40ab + 16b^2)(5a + 4b)
V = 125a^3 + 100a^2b + 200a^2b + 160ab^2 + 80ab^2 + 64b^3
V = 125a^3 + 300a^2b + 240ab^2 + 64b^3
The first step in graphing a linear inequality is to graph the linear equality. The equation -x + 4y = -8 is equivalent to 4y = x - 8, which is equivalent to
. This is the equation for the line in slope-intercept form, so the line will have a slope of 1/4 and a y-intercept of -2 (see the first image). Notice that the line is solid, rather than dotted. This represents that points on the line are included in the solution, because the inequality sign is ≥, which is not a strict equality (< or >).
Next, we need to figure out which side to shade. To do so, simply pick any point (I like to use the point (0,0) because it makes the calculations easy) and see whether it satisfies the inequality. If it does, shade the side with that point, and if not, shade the opposite side of the graph.
Here we see that the point (0,0) does satisfy the inequality, since -(0) + 4(0) is 0, and 0 ≥ -8, so the top half of the graph should be shaded (see the second image).
Answer: the speed of the submarine is 5miles per hour
Step-by-step explanation:
The submarine left Hawaii two hours before the aircraft carrier.
Let x = the speed of the submarine
The aircraft carrier traveled at 25 mph for nine hours.
After this time the vessels were 280 miles apart. This means that when they became 280 miles apart, the aircraft carrier has travelled for 9 hours. If the submarine was ahead of the aircraft carrier with 2 hours, that means that the submarine travelled 9 + 2 = 11 hours
Distance travelled = speed × time
Distance travelled by submarine will be 11 × x = 11x miles per hour
Distance travelled by aircraft carrier will be 25 × 9 = 225 miles per hour
If they are 280 miles apart, this would be their total distance. Therefore,
225 + 11x = 280
11x = 280 - 225 = 55
x = 55/11 = 5miles per hour